ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. 67,   1   (1998)
pp.   181-195

THE FINITE VOLUME METHOD FOR AN ELLIPTIC-PARABOLIC EQUATION
R. EYMARD, M. GUTNIC and D. HILHORST


Abstract.  In this note we prove the convergence of a finite volume scheme for the discretization of an elliptic-parabolic problem, namely the nonlinear diffusion equation $c(u)_t-\Delta u = 0$, together with Dirichlet boundary conditions and an initial condition. This is done by means of a priori estimates in $L^2$ and the use of Kolmogorov's theorem on relative compactness of subsets of $L^2$.

AMS subject classification
Keywords

Download:     Adobe PDF     Compressed Postscript      

Acta Mathematica Universitatis Comenianae
Institute of Applied Mathematics
Faculty of Mathematics, Physics and Informatics
Comenius University
842 48 Bratislava, Slovak Republic  

Telephone: + 421-2-60295111 Fax: + 421-2-65425882  
e-Mail: amuc@fmph.uniba.sk   Internet: www.iam.fmph.uniba.sk/amuc

© Copyright 2001, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE